Use the Laplace transform to solve the following initial value problem: , First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation and then solve for . $\frac{1}{s^3 2s^2} \frac{3}{s 2}$ Now take the inverse Laplace transform of both sides of the previous equation and solve for .

An electrical motor raises a 50kg load at a construct velencity .calculate the power of the motor, if it takes 40sec to raise the load through a height of 24m(take g =9.8n/g)

The temperature of air decreases as it is compressed by an adiabatic compressor. a)- true b)- false

Adouble-strand no. 60 roller chain is used to transmit power between a 13-tooth driving sprocket rotating at 300 rev/min and a 52-tooth driven sprocket. a) what is the allowable horsepower of this drive? b) estimate the center-to-center distance if the chain length is 82 pitches. c) estimate the torque and bending force on the driving shaft by the chain if the actual horsepower transmitted is 30 percent less than the corrected (allowable) power.